Accelerated Life Tests under Gamma Stress Distribution

스트레스함수가 감마분포인 가속수명시험

  • Published : 2002.09.01

Abstract

This paper presents accelerated life tests for Type I censoring data under probabilistic stresses. Probabilistic stress, S, is the random variable for stress influenced by test environments, test equipments, sampling devices and use conditions. The hazard rate, $\theta$ is a random variable of environments and a function of probabilistic stress. In detail, it is assumed that the hazard rate is linear function of the stress, the general stress distribution is a gamma distribution and the life distribution for the given hazard rate, $\theta$is an exponential distribution. Maximum likelihood estimators of model parameters are obtained, and the mean life in use stress condition is estimated. A hypothetical example is given to show its applicability.

Keywords

References

  1. Bai, D. S. and H. J. Yun, 'Accelerated Life Tests for Products of Unequal Size', IEEE Trans. Rel., Vol. 45, No. 4, pp. 611-618, 1996 https://doi.org/10.1109/24.556583
  2. Nelson, W., 'Analysis of Accelerated Life Test Data-Part I : The Arrhenius Model and Graphical Methods', IEEE Trans. Rel., Vol. EI-6, No. 4, pp. 165-181, 1971
  3. Nelson, W., 'Analysis of Accelerated Life Test Data-Part II: Numerical Methods and Test Planning', IEEE Trans. Rel., Vol. EI-7, No. 1, pp. 36-55, 1972
  4. Nelson, W., 'Analysis of Accelerated Life Test Data-Part III: Product Comparisons and Checks on the Validity of the Model and Data', IEEE Trans. Rel., Vol. EI-7, No. 2, pp. 99-119, 1972
  5. Nelson, W., 'Accelerated Life Testing-Step-Stress Model and Data Analyses', IEEE Trans. ReI., Vol. R-29, No. 2, pp. 103-108, 1980 https://doi.org/10.1109/TR.1980.5220742
  6. Seo, S. K. and B. J. Yum, 'Accelerated Life Test Plans under Intermittent Inspection and Type- I Censoring: The Case of Weibull Failure Distribution', Nav. Res. Log., Vol. 38, pp. 1-22, 1991 https://doi.org/10.1002/1520-6750(199102)38:1<1::AID-NAV3220380103>3.0.CO;2-3
  7. Singpurwalla, N. D., 'Inference from Accelerated Life Tests When Observations Are Obtained from Censored Samples', Technometrics, Vol. 13, No. 1, pp. 161-170, 1971 https://doi.org/10.2307/1267083
  8. Singpurwalla, N. D., 'A Problem in Accelerated Life Testing', J, Amer. Statist. Assoc., Vol. 66, No. 336, pp. 841-845, 1971 https://doi.org/10.2307/2284238
  9. Singpurwalla, N. D., 'Inference from Accelerated Life Tests Using Arrhenius Type Re-Parameterizations', Technometrics, Vol. 15, No. 2, pp. 289-299, 1973 https://doi.org/10.2307/1266989
  10. Singpurwalla, N. D., V. C. Castellino, and D. Y. Goldschen, 'Inference from Accelerated Life Tests Using Eyring Type Re-Parameterizations', Nav. Res. Log. Q., Vol. 22, pp. 289-296, 1975 https://doi.org/10.1002/nav.3800220207
  11. Won, Y. C., 'Accelerated Life Tests under Uniform Stress Distribution', Journal of the Safety Management & Science, Vol. 2, No.2, pp.71-83, 2000
  12. Yin X. K. and B. J. Sheng, 'Some Aspects of Accelerated Life Testing by Progressive Stress', IEEE Trans. ReI., Vol. R-36, No. 1, pp. 150-155, 1987 https://doi.org/10.1109/TR.1987.5222320
  13. Yum, B. J. and S. C. Choi, 'Optimal Design of Accelerated Life Tests under Periodic Inspection', Nav. Res. Log., Vol. 36, pp. 779-795, 1989 https://doi.org/10.1002/1520-6750(198912)36:6<779::AID-NAV3220360604>3.0.CO;2-2